Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1521,4,Mod(1,1521)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1521, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1521.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1521 = 3^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1521.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(89.7419051187\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 70x^{8} + 1645x^{6} - 14700x^{4} + 44100x^{2} - 27648 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 39) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(5.36472\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1521.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.36472 | 1.89672 | 0.948358 | − | 0.317201i | \(-0.102743\pi\) | ||||
0.948358 | + | 0.317201i | \(0.102743\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 20.7803 | 2.59753 | ||||||||
\(5\) | −2.69631 | −0.241165 | −0.120583 | − | 0.992703i | \(-0.538476\pi\) | ||||
−0.120583 | + | 0.992703i | \(0.538476\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 15.2025 | 0.820856 | 0.410428 | − | 0.911893i | \(-0.365379\pi\) | ||||
0.410428 | + | 0.911893i | \(0.365379\pi\) | |||||||
\(8\) | 68.5626 | 3.03007 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −14.4650 | −0.457423 | ||||||||
\(11\) | 66.8848 | 1.83332 | 0.916661 | − | 0.399666i | \(-0.130874\pi\) | ||||
0.916661 | + | 0.399666i | \(0.130874\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 81.5570 | 1.55693 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 201.577 | 3.14965 | ||||||||
\(17\) | −4.16354 | −0.0594004 | −0.0297002 | − | 0.999559i | \(-0.509455\pi\) | ||||
−0.0297002 | + | 0.999559i | \(0.509455\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.0850 | 0.314963 | 0.157482 | − | 0.987522i | \(-0.449662\pi\) | ||||
0.157482 | + | 0.987522i | \(0.449662\pi\) | |||||||
\(20\) | −56.0301 | −0.626436 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 358.819 | 3.47729 | ||||||||
\(23\) | −47.3242 | −0.429034 | −0.214517 | − | 0.976720i | \(-0.568818\pi\) | ||||
−0.214517 | + | 0.976720i | \(0.568818\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −117.730 | −0.941839 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 315.911 | 2.13220 | ||||||||
\(29\) | −257.007 | −1.64569 | −0.822845 | − | 0.568266i | \(-0.807614\pi\) | ||||
−0.822845 | + | 0.568266i | \(0.807614\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 206.242 | 1.19491 | 0.597455 | − | 0.801903i | \(-0.296179\pi\) | ||||
0.597455 | + | 0.801903i | \(0.296179\pi\) | |||||||
\(32\) | 532.906 | 2.94392 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −22.3362 | −0.112666 | ||||||||
\(35\) | −40.9906 | −0.197962 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 175.686 | 0.780611 | 0.390305 | − | 0.920685i | \(-0.372369\pi\) | ||||
0.390305 | + | 0.920685i | \(0.372369\pi\) | |||||||
\(38\) | 139.939 | 0.597396 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −184.866 | −0.730748 | ||||||||
\(41\) | −156.463 | −0.595984 | −0.297992 | − | 0.954568i | \(-0.596317\pi\) | ||||
−0.297992 | + | 0.954568i | \(0.596317\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 51.9845 | 0.184362 | 0.0921809 | − | 0.995742i | \(-0.470616\pi\) | ||||
0.0921809 | + | 0.995742i | \(0.470616\pi\) | |||||||
\(44\) | 1389.88 | 4.76211 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −253.881 | −0.813755 | ||||||||
\(47\) | 354.222 | 1.09933 | 0.549666 | − | 0.835384i | \(-0.314755\pi\) | ||||
0.549666 | + | 0.835384i | \(0.314755\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −111.885 | −0.326196 | ||||||||
\(50\) | −631.588 | −1.78640 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.4723 | 0.0271412 | 0.0135706 | − | 0.999908i | \(-0.495680\pi\) | ||||
0.0135706 | + | 0.999908i | \(0.495680\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −180.342 | −0.442134 | ||||||||
\(56\) | 1042.32 | 2.48725 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1378.77 | −3.12141 | ||||||||
\(59\) | −445.114 | −0.982185 | −0.491092 | − | 0.871107i | \(-0.663402\pi\) | ||||
−0.491092 | + | 0.871107i | \(0.663402\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 119.696 | 0.251238 | 0.125619 | − | 0.992079i | \(-0.459908\pi\) | ||||
0.125619 | + | 0.992079i | \(0.459908\pi\) | |||||||
\(62\) | 1106.43 | 2.26640 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1246.28 | 2.43413 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −22.4078 | −0.0408589 | −0.0204294 | − | 0.999791i | \(-0.506503\pi\) | ||||
−0.0204294 | + | 0.999791i | \(0.506503\pi\) | |||||||
\(68\) | −86.5195 | −0.154295 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −219.903 | −0.375478 | ||||||||
\(71\) | −285.207 | −0.476731 | −0.238365 | − | 0.971176i | \(-0.576612\pi\) | ||||
−0.238365 | + | 0.971176i | \(0.576612\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 740.989 | 1.18803 | 0.594015 | − | 0.804454i | \(-0.297542\pi\) | ||||
0.594015 | + | 0.804454i | \(0.297542\pi\) | |||||||
\(74\) | 942.507 | 1.48060 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 542.053 | 0.818128 | ||||||||
\(77\) | 1016.81 | 1.50489 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −547.679 | −0.779983 | −0.389992 | − | 0.920818i | \(-0.627522\pi\) | ||||
−0.389992 | + | 0.920818i | \(0.627522\pi\) | |||||||
\(80\) | −543.516 | −0.759586 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −839.378 | −1.13041 | ||||||||
\(83\) | −603.056 | −0.797518 | −0.398759 | − | 0.917056i | \(-0.630559\pi\) | ||||
−0.398759 | + | 0.917056i | \(0.630559\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.2262 | 0.0143253 | ||||||||
\(86\) | 278.882 | 0.349682 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4585.80 | 5.55509 | ||||||||
\(89\) | −215.668 | −0.256863 | −0.128431 | − | 0.991718i | \(-0.540994\pi\) | ||||
−0.128431 | + | 0.991718i | \(0.540994\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −983.409 | −1.11443 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1900.31 | 2.08512 | ||||||||
\(95\) | −70.3333 | −0.0759583 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1447.50 | 1.51517 | 0.757586 | − | 0.652735i | \(-0.226378\pi\) | ||||
0.757586 | + | 0.652735i | \(0.226378\pi\) | |||||||
\(98\) | −600.233 | −0.618700 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2446.46 | −2.44646 | ||||||||
\(101\) | 883.450 | 0.870362 | 0.435181 | − | 0.900343i | \(-0.356684\pi\) | ||||
0.435181 | + | 0.900343i | \(0.356684\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1251.74 | 1.19745 | 0.598726 | − | 0.800954i | \(-0.295674\pi\) | ||||
0.598726 | + | 0.800954i | \(0.295674\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 56.1812 | 0.0514792 | ||||||||
\(107\) | 341.614 | 0.308645 | 0.154323 | − | 0.988021i | \(-0.450681\pi\) | ||||
0.154323 | + | 0.988021i | \(0.450681\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 775.177 | 0.681179 | 0.340589 | − | 0.940212i | \(-0.389373\pi\) | ||||
0.340589 | + | 0.940212i | \(0.389373\pi\) | |||||||
\(110\) | −967.487 | −0.838603 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3064.47 | 2.58541 | ||||||||
\(113\) | −1279.05 | −1.06480 | −0.532402 | − | 0.846492i | \(-0.678710\pi\) | ||||
−0.532402 | + | 0.846492i | \(0.678710\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 127.601 | 0.103468 | ||||||||
\(116\) | −5340.67 | −4.27473 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2387.91 | −1.86293 | ||||||||
\(119\) | −63.2961 | −0.0487592 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3142.58 | 2.36107 | ||||||||
\(122\) | 642.137 | 0.476528 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4285.77 | 3.10382 | ||||||||
\(125\) | 654.476 | 0.468305 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1113.82 | −0.778233 | −0.389117 | − | 0.921188i | \(-0.627220\pi\) | ||||
−0.389117 | + | 0.921188i | \(0.627220\pi\) | |||||||
\(128\) | 2422.68 | 1.67294 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2100.12 | −1.40068 | −0.700339 | − | 0.713811i | \(-0.746968\pi\) | ||||
−0.700339 | + | 0.713811i | \(0.746968\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 396.556 | 0.258540 | ||||||||
\(134\) | −120.211 | −0.0774977 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −285.463 | −0.179987 | ||||||||
\(137\) | 1205.02 | 0.751471 | 0.375736 | − | 0.926727i | \(-0.377390\pi\) | ||||
0.375736 | + | 0.926727i | \(0.377390\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 322.890 | 0.197030 | 0.0985149 | − | 0.995136i | \(-0.468591\pi\) | ||||
0.0985149 | + | 0.995136i | \(0.468591\pi\) | |||||||
\(140\) | −851.796 | −0.514213 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1530.06 | −0.904223 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 692.971 | 0.396884 | ||||||||
\(146\) | 3975.20 | 2.25336 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3650.80 | 2.02766 | ||||||||
\(149\) | −1128.86 | −0.620669 | −0.310335 | − | 0.950627i | \(-0.600441\pi\) | ||||
−0.310335 | + | 0.950627i | \(0.600441\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2940.44 | −1.58470 | −0.792350 | − | 0.610066i | \(-0.791143\pi\) | ||||
−0.792350 | + | 0.610066i | \(0.791143\pi\) | |||||||
\(152\) | 1788.46 | 0.954361 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5454.93 | 2.85436 | ||||||||
\(155\) | −556.093 | −0.288171 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 629.388 | 0.319940 | 0.159970 | − | 0.987122i | \(-0.448860\pi\) | ||||
0.159970 | + | 0.987122i | \(0.448860\pi\) | |||||||
\(158\) | −2938.15 | −1.47941 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1436.88 | −0.709972 | ||||||||
\(161\) | −719.444 | −0.352175 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −394.912 | −0.189766 | −0.0948832 | − | 0.995488i | \(-0.530248\pi\) | ||||
−0.0948832 | + | 0.995488i | \(0.530248\pi\) | |||||||
\(164\) | −3251.33 | −1.54809 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3235.23 | −1.51267 | ||||||||
\(167\) | 151.860 | 0.0703669 | 0.0351834 | − | 0.999381i | \(-0.488798\pi\) | ||||
0.0351834 | + | 0.999381i | \(0.488798\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 60.2255 | 0.0271711 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1080.25 | 0.478886 | ||||||||
\(173\) | −538.813 | −0.236793 | −0.118397 | − | 0.992966i | \(-0.537775\pi\) | ||||
−0.118397 | + | 0.992966i | \(0.537775\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1789.78 | −0.773114 | ||||||||
\(176\) | 13482.5 | 5.77432 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1157.00 | −0.487196 | ||||||||
\(179\) | 2220.80 | 0.927319 | 0.463659 | − | 0.886014i | \(-0.346536\pi\) | ||||
0.463659 | + | 0.886014i | \(0.346536\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3822.78 | −1.56986 | −0.784932 | − | 0.619582i | \(-0.787302\pi\) | ||||
−0.784932 | + | 0.619582i | \(0.787302\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3244.67 | −1.30000 | ||||||||
\(185\) | −473.704 | −0.188256 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −278.478 | −0.108900 | ||||||||
\(188\) | 7360.84 | 2.85555 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −377.319 | −0.144071 | ||||||||
\(191\) | −3464.19 | −1.31236 | −0.656178 | − | 0.754606i | \(-0.727828\pi\) | ||||
−0.656178 | + | 0.754606i | \(0.727828\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4697.40 | 1.75195 | 0.875975 | − | 0.482357i | \(-0.160219\pi\) | ||||
0.875975 | + | 0.482357i | \(0.160219\pi\) | |||||||
\(194\) | 7765.46 | 2.87385 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2325.00 | −0.847304 | ||||||||
\(197\) | 2887.89 | 1.04443 | 0.522217 | − | 0.852813i | \(-0.325105\pi\) | ||||
0.522217 | + | 0.852813i | \(0.325105\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 63.0092 | 0.0224453 | 0.0112226 | − | 0.999937i | \(-0.496428\pi\) | ||||
0.0112226 | + | 0.999937i | \(0.496428\pi\) | |||||||
\(200\) | −8071.87 | −2.85384 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4739.47 | 1.65083 | ||||||||
\(203\) | −3907.14 | −1.35087 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 421.872 | 0.143731 | ||||||||
\(206\) | 6715.24 | 2.27123 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1744.69 | 0.577429 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1049.70 | −0.342484 | −0.171242 | − | 0.985229i | \(-0.554778\pi\) | ||||
−0.171242 | + | 0.985229i | \(0.554778\pi\) | |||||||
\(212\) | 217.618 | 0.0705002 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1832.66 | 0.585412 | ||||||||
\(215\) | −140.166 | −0.0444617 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3135.39 | 0.980848 | ||||||||
\(218\) | 4158.61 | 1.29200 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3747.56 | −1.14846 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2313.49 | 0.694722 | 0.347361 | − | 0.937732i | \(-0.387078\pi\) | ||||
0.347361 | + | 0.937732i | \(0.387078\pi\) | |||||||
\(224\) | 8101.49 | 2.41653 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6861.74 | −2.01963 | ||||||||
\(227\) | −3799.46 | −1.11092 | −0.555460 | − | 0.831543i | \(-0.687458\pi\) | ||||
−0.555460 | + | 0.831543i | \(0.687458\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4321.07 | −1.24692 | −0.623459 | − | 0.781856i | \(-0.714273\pi\) | ||||
−0.623459 | + | 0.781856i | \(0.714273\pi\) | |||||||
\(230\) | 684.543 | 0.196250 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −17621.1 | −4.98655 | ||||||||
\(233\) | −5279.77 | −1.48450 | −0.742251 | − | 0.670122i | \(-0.766242\pi\) | ||||
−0.742251 | + | 0.670122i | \(0.766242\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −955.094 | −0.265121 | ||||||||
\(236\) | −9249.59 | −2.55126 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −339.566 | −0.0924823 | ||||||||
\(239\) | −1547.92 | −0.418939 | −0.209469 | − | 0.977815i | \(-0.567174\pi\) | ||||
−0.209469 | + | 0.977815i | \(0.567174\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4918.01 | −1.31451 | −0.657255 | − | 0.753669i | \(-0.728282\pi\) | ||||
−0.657255 | + | 0.753669i | \(0.728282\pi\) | |||||||
\(242\) | 16859.1 | 4.47828 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2487.32 | 0.652600 | ||||||||
\(245\) | 301.677 | 0.0786671 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 14140.5 | 3.62066 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3511.08 | 0.888241 | ||||||||
\(251\) | −1155.78 | −0.290646 | −0.145323 | − | 0.989384i | \(-0.546422\pi\) | ||||
−0.145323 | + | 0.989384i | \(0.546422\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3165.27 | −0.786556 | ||||||||
\(254\) | −5975.34 | −1.47609 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3026.80 | 0.738965 | ||||||||
\(257\) | −2351.95 | −0.570859 | −0.285429 | − | 0.958400i | \(-0.592136\pi\) | ||||
−0.285429 | + | 0.958400i | \(0.592136\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2670.86 | 0.640769 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −11266.6 | −2.65669 | ||||||||
\(263\) | −5521.88 | −1.29465 | −0.647326 | − | 0.762213i | \(-0.724113\pi\) | ||||
−0.647326 | + | 0.762213i | \(0.724113\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −28.2367 | −0.00654553 | ||||||||
\(266\) | 2127.41 | 0.490376 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −465.639 | −0.106132 | ||||||||
\(269\) | −3916.95 | −0.887810 | −0.443905 | − | 0.896074i | \(-0.646407\pi\) | ||||
−0.443905 | + | 0.896074i | \(0.646407\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2777.53 | −0.622593 | −0.311297 | − | 0.950313i | \(-0.600763\pi\) | ||||
−0.311297 | + | 0.950313i | \(0.600763\pi\) | |||||||
\(272\) | −839.276 | −0.187090 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6464.58 | 1.42533 | ||||||||
\(275\) | −7874.34 | −1.72669 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6583.08 | 1.42794 | 0.713969 | − | 0.700177i | \(-0.246896\pi\) | ||||
0.713969 | + | 0.700177i | \(0.246896\pi\) | |||||||
\(278\) | 1732.21 | 0.373710 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2810.42 | −0.599839 | ||||||||
\(281\) | −2871.66 | −0.609640 | −0.304820 | − | 0.952410i | \(-0.598596\pi\) | ||||
−0.304820 | + | 0.952410i | \(0.598596\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7518.04 | 1.57916 | 0.789578 | − | 0.613651i | \(-0.210300\pi\) | ||||
0.789578 | + | 0.613651i | \(0.210300\pi\) | |||||||
\(284\) | −5926.69 | −1.23832 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2378.62 | −0.489217 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4895.66 | −0.996472 | ||||||||
\(290\) | 3717.60 | 0.752776 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15397.9 | 3.08595 | ||||||||
\(293\) | −4506.57 | −0.898555 | −0.449278 | − | 0.893392i | \(-0.648319\pi\) | ||||
−0.449278 | + | 0.893392i | \(0.648319\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1200.17 | 0.236869 | ||||||||
\(296\) | 12045.5 | 2.36530 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6056.02 | −1.17723 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 790.292 | 0.151335 | ||||||||
\(302\) | −15774.7 | −3.00573 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5258.15 | 0.992024 | ||||||||
\(305\) | −322.738 | −0.0605900 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9538.89 | 1.77333 | 0.886667 | − | 0.462409i | \(-0.153015\pi\) | ||||
0.886667 | + | 0.462409i | \(0.153015\pi\) | |||||||
\(308\) | 21129.7 | 3.90901 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2983.29 | −0.546578 | ||||||||
\(311\) | 7466.28 | 1.36133 | 0.680666 | − | 0.732594i | \(-0.261691\pi\) | ||||
0.680666 | + | 0.732594i | \(0.261691\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1821.65 | −0.328964 | −0.164482 | − | 0.986380i | \(-0.552595\pi\) | ||||
−0.164482 | + | 0.986380i | \(0.552595\pi\) | |||||||
\(314\) | 3376.49 | 0.606836 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −11380.9 | −2.02603 | ||||||||
\(317\) | −3125.14 | −0.553708 | −0.276854 | − | 0.960912i | \(-0.589292\pi\) | ||||
−0.276854 | + | 0.960912i | \(0.589292\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −17189.9 | −3.01708 | ||||||||
\(320\) | −3360.35 | −0.587029 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3859.62 | −0.667976 | ||||||||
\(323\) | −108.606 | −0.0187090 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2118.60 | −0.359933 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10727.5 | −1.80587 | ||||||||
\(329\) | 5385.05 | 0.902394 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1553.67 | −0.257999 | −0.128999 | − | 0.991645i | \(-0.541177\pi\) | ||||
−0.128999 | + | 0.991645i | \(0.541177\pi\) | |||||||
\(332\) | −12531.7 | −2.07158 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 814.686 | 0.133466 | ||||||||
\(335\) | 60.4183 | 0.00985375 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3190.43 | −0.515709 | −0.257855 | − | 0.966184i | \(-0.583016\pi\) | ||||
−0.257855 | + | 0.966184i | \(0.583016\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 233.283 | 0.0372105 | ||||||||
\(341\) | 13794.5 | 2.19065 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6915.37 | −1.08862 | ||||||||
\(344\) | 3564.19 | 0.558629 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2890.59 | −0.449130 | ||||||||
\(347\) | 5718.68 | 0.884712 | 0.442356 | − | 0.896840i | \(-0.354143\pi\) | ||||
0.442356 | + | 0.896840i | \(0.354143\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3328.46 | −0.510511 | −0.255256 | − | 0.966874i | \(-0.582160\pi\) | ||||
−0.255256 | + | 0.966874i | \(0.582160\pi\) | |||||||
\(350\) | −9601.70 | −1.46638 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 35643.4 | 5.39715 | ||||||||
\(353\) | 12306.5 | 1.85555 | 0.927774 | − | 0.373142i | \(-0.121719\pi\) | ||||
0.927774 | + | 0.373142i | \(0.121719\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 769.008 | 0.114971 | ||||||||
\(356\) | −4481.64 | −0.667210 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 11914.0 | 1.75886 | ||||||||
\(359\) | −8539.97 | −1.25549 | −0.627747 | − | 0.778418i | \(-0.716023\pi\) | ||||
−0.627747 | + | 0.778418i | \(0.716023\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6178.57 | −0.900798 | ||||||||
\(362\) | −20508.2 | −2.97759 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1997.94 | −0.286512 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2496.65 | 0.355107 | 0.177553 | − | 0.984111i | \(-0.443182\pi\) | ||||
0.177553 | + | 0.984111i | \(0.443182\pi\) | |||||||
\(368\) | −9539.49 | −1.35130 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2541.29 | −0.357069 | ||||||||
\(371\) | 159.205 | 0.0222790 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1142.91 | −0.158653 | −0.0793264 | − | 0.996849i | \(-0.525277\pi\) | ||||
−0.0793264 | + | 0.996849i | \(0.525277\pi\) | |||||||
\(374\) | −1493.96 | −0.206552 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 24286.4 | 3.33105 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12181.8 | −1.65102 | −0.825512 | − | 0.564384i | \(-0.809114\pi\) | ||||
−0.825512 | + | 0.564384i | \(0.809114\pi\) | |||||||
\(380\) | −1461.54 | −0.197304 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −18584.4 | −2.48917 | ||||||||
\(383\) | 10180.6 | 1.35824 | 0.679118 | − | 0.734029i | \(-0.262362\pi\) | ||||
0.679118 | + | 0.734029i | \(0.262362\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2741.65 | −0.362928 | ||||||||
\(386\) | 25200.3 | 3.32295 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 30079.5 | 3.93571 | ||||||||
\(389\) | −5845.83 | −0.761941 | −0.380971 | − | 0.924587i | \(-0.624410\pi\) | ||||
−0.380971 | + | 0.924587i | \(0.624410\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 197.036 | 0.0254848 | ||||||||
\(392\) | −7671.13 | −0.988395 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 15492.7 | 1.98100 | ||||||||
\(395\) | 1476.71 | 0.188105 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2500.92 | −0.316166 | −0.158083 | − | 0.987426i | \(-0.550531\pi\) | ||||
−0.158083 | + | 0.987426i | \(0.550531\pi\) | |||||||
\(398\) | 338.027 | 0.0425723 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −23731.7 | −2.96646 | ||||||||
\(401\) | 9189.25 | 1.14436 | 0.572181 | − | 0.820127i | \(-0.306098\pi\) | ||||
0.572181 | + | 0.820127i | \(0.306098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 18358.3 | 2.26080 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20960.7 | −2.56223 | ||||||||
\(407\) | 11750.7 | 1.43111 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9214.38 | 1.11399 | 0.556995 | − | 0.830516i | \(-0.311954\pi\) | ||||
0.556995 | + | 0.830516i | \(0.311954\pi\) | |||||||
\(410\) | 2263.23 | 0.272617 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 26011.5 | 3.11042 | ||||||||
\(413\) | −6766.83 | −0.806232 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1626.03 | 0.192334 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 9359.78 | 1.09522 | ||||||||
\(419\) | 6494.41 | 0.757214 | 0.378607 | − | 0.925558i | \(-0.376403\pi\) | ||||
0.378607 | + | 0.925558i | \(0.376403\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3059.56 | 0.354190 | 0.177095 | − | 0.984194i | \(-0.443330\pi\) | ||||
0.177095 | + | 0.984194i | \(0.443330\pi\) | |||||||
\(422\) | −5631.33 | −0.649595 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 718.010 | 0.0822398 | ||||||||
\(425\) | 490.173 | 0.0559456 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1819.68 | 0.206230 | ||||||||
\(428\) | 7098.82 | 0.801716 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −751.954 | −0.0843313 | ||||||||
\(431\) | −7937.05 | −0.887040 | −0.443520 | − | 0.896264i | \(-0.646271\pi\) | ||||
−0.443520 | + | 0.896264i | \(0.646271\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7294.37 | 0.809573 | 0.404786 | − | 0.914411i | \(-0.367346\pi\) | ||||
0.404786 | + | 0.914411i | \(0.367346\pi\) | |||||||
\(434\) | 16820.5 | 1.86039 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 16108.4 | 1.76938 | ||||||||
\(437\) | −1234.45 | −0.135130 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15214.7 | 1.65412 | 0.827059 | − | 0.562115i | \(-0.190012\pi\) | ||||
0.827059 | + | 0.562115i | \(0.190012\pi\) | |||||||
\(440\) | −12364.7 | −1.33970 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1517.05 | −0.162703 | −0.0813515 | − | 0.996685i | \(-0.525924\pi\) | ||||
−0.0813515 | + | 0.996685i | \(0.525924\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 581.509 | 0.0619464 | ||||||||
\(446\) | 12411.3 | 1.31769 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 18946.5 | 1.99807 | ||||||||
\(449\) | 705.247 | 0.0741262 | 0.0370631 | − | 0.999313i | \(-0.488200\pi\) | ||||
0.0370631 | + | 0.999313i | \(0.488200\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10465.0 | −1.09263 | ||||||||
\(452\) | −26579.0 | −2.76586 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −20383.1 | −2.10710 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7277.73 | −0.744940 | −0.372470 | − | 0.928044i | \(-0.621489\pi\) | ||||
−0.372470 | + | 0.928044i | \(0.621489\pi\) | |||||||
\(458\) | −23181.4 | −2.36505 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2651.58 | 0.268762 | ||||||||
\(461\) | −1961.88 | −0.198208 | −0.0991041 | − | 0.995077i | \(-0.531598\pi\) | ||||
−0.0991041 | + | 0.995077i | \(0.531598\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10374.1 | −1.04131 | −0.520653 | − | 0.853768i | \(-0.674311\pi\) | ||||
−0.520653 | + | 0.853768i | \(0.674311\pi\) | |||||||
\(464\) | −51806.8 | −5.18334 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −28324.5 | −2.81568 | ||||||||
\(467\) | −8788.92 | −0.870883 | −0.435442 | − | 0.900217i | \(-0.643408\pi\) | ||||
−0.435442 | + | 0.900217i | \(0.643408\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −340.653 | −0.0335392 | ||||||||
\(470\) | −5123.82 | −0.502860 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −30518.2 | −2.97609 | ||||||||
\(473\) | 3476.97 | 0.337995 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3070.98 | −0.296645 | ||||||||
\(476\) | −1315.31 | −0.126654 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8304.14 | −0.794608 | ||||||||
\(479\) | 11141.7 | 1.06279 | 0.531394 | − | 0.847125i | \(-0.321668\pi\) | ||||
0.531394 | + | 0.847125i | \(0.321668\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −26383.8 | −2.49325 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 65303.7 | 6.13295 | ||||||||
\(485\) | −3902.92 | −0.365407 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19640.5 | −1.82750 | −0.913752 | − | 0.406273i | \(-0.866828\pi\) | ||||
−0.913752 | + | 0.406273i | \(0.866828\pi\) | |||||||
\(488\) | 8206.69 | 0.761269 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1618.41 | 0.149209 | ||||||||
\(491\) | 3410.31 | 0.313453 | 0.156726 | − | 0.987642i | \(-0.449906\pi\) | ||||
0.156726 | + | 0.987642i | \(0.449906\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1070.06 | 0.0977546 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 41573.8 | 3.76354 | ||||||||
\(497\) | −4335.86 | −0.391327 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5032.44 | −0.451469 | −0.225735 | − | 0.974189i | \(-0.572478\pi\) | ||||
−0.225735 | + | 0.974189i | \(0.572478\pi\) | |||||||
\(500\) | 13600.2 | 1.21644 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6200.44 | −0.551274 | ||||||||
\(503\) | −17189.4 | −1.52373 | −0.761866 | − | 0.647735i | \(-0.775716\pi\) | ||||
−0.761866 | + | 0.647735i | \(0.775716\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2382.06 | −0.209901 | ||||||||
\(506\) | −16980.8 | −1.49187 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −23145.5 | −2.02149 | ||||||||
\(509\) | 930.560 | 0.0810341 | 0.0405170 | − | 0.999179i | \(-0.487099\pi\) | ||||
0.0405170 | + | 0.999179i | \(0.487099\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11264.9 | 0.975201 | ||||||||
\(512\) | −3143.50 | −0.271337 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −12617.6 | −1.08276 | ||||||||
\(515\) | −3375.08 | −0.288784 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23692.1 | 2.01543 | ||||||||
\(518\) | 14328.4 | 1.21536 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9869.60 | 0.829933 | 0.414966 | − | 0.909837i | \(-0.363793\pi\) | ||||
0.414966 | + | 0.909837i | \(0.363793\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21420.6 | −1.79093 | −0.895466 | − | 0.445129i | \(-0.853158\pi\) | ||||
−0.895466 | + | 0.445129i | \(0.853158\pi\) | |||||||
\(524\) | −43641.1 | −3.63831 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −29623.4 | −2.45559 | ||||||||
\(527\) | −858.697 | −0.0709781 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9927.42 | −0.815930 | ||||||||
\(530\) | −151.482 | −0.0124150 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 8240.54 | 0.671565 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −921.097 | −0.0744345 | ||||||||
\(536\) | −1536.34 | −0.123805 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −21013.4 | −1.68392 | ||||||||
\(539\) | −7483.41 | −0.598021 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7771.50 | 0.617602 | 0.308801 | − | 0.951127i | \(-0.400072\pi\) | ||||
0.308801 | + | 0.951127i | \(0.400072\pi\) | |||||||
\(542\) | −14900.7 | −1.18088 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2218.78 | −0.174870 | ||||||||
\(545\) | −2090.12 | −0.164277 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15577.5 | −1.21763 | −0.608817 | − | 0.793310i | \(-0.708356\pi\) | ||||
−0.608817 | + | 0.793310i | \(0.708356\pi\) | |||||||
\(548\) | 25040.6 | 1.95197 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −42243.7 | −3.27505 | ||||||||
\(551\) | −6704.02 | −0.518332 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8326.07 | −0.640254 | ||||||||
\(554\) | 35316.4 | 2.70840 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6709.74 | 0.511792 | ||||||||
\(557\) | 22804.5 | 1.73475 | 0.867377 | − | 0.497652i | \(-0.165804\pi\) | ||||
0.867377 | + | 0.497652i | \(0.165804\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −8262.78 | −0.623511 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −15405.7 | −1.15631 | ||||||||
\(563\) | 3517.41 | 0.263306 | 0.131653 | − | 0.991296i | \(-0.457972\pi\) | ||||
0.131653 | + | 0.991296i | \(0.457972\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3448.71 | 0.256794 | ||||||||
\(566\) | 40332.2 | 2.99521 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −19554.6 | −1.44453 | ||||||||
\(569\) | 6093.44 | 0.448946 | 0.224473 | − | 0.974480i | \(-0.427934\pi\) | ||||
0.224473 | + | 0.974480i | \(0.427934\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10460.2 | 0.766630 | 0.383315 | − | 0.923618i | \(-0.374782\pi\) | ||||
0.383315 | + | 0.923618i | \(0.374782\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −12760.6 | −0.927906 | ||||||||
\(575\) | 5571.47 | 0.404081 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9648.19 | −0.696117 | −0.348058 | − | 0.937473i | \(-0.613159\pi\) | ||||
−0.348058 | + | 0.937473i | \(0.613159\pi\) | |||||||
\(578\) | −26263.9 | −1.89002 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 14400.1 | 1.03092 | ||||||||
\(581\) | −9167.93 | −0.654647 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 700.440 | 0.0497586 | ||||||||
\(584\) | 50804.1 | 3.59981 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −24176.5 | −1.70430 | ||||||||
\(587\) | −2170.73 | −0.152633 | −0.0763166 | − | 0.997084i | \(-0.524316\pi\) | ||||
−0.0763166 | + | 0.997084i | \(0.524316\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5379.82 | 0.376353 | ||||||||
\(590\) | 6438.56 | 0.449274 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 35414.3 | 2.45865 | ||||||||
\(593\) | −22885.9 | −1.58484 | −0.792421 | − | 0.609975i | \(-0.791180\pi\) | ||||
−0.792421 | + | 0.609975i | \(0.791180\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 170.666 | 0.0117590 | ||||||||
\(596\) | −23458.0 | −1.61221 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 23978.7 | 1.63563 | 0.817815 | − | 0.575482i | \(-0.195185\pi\) | ||||
0.817815 | + | 0.575482i | \(0.195185\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12873.2 | 0.873728 | 0.436864 | − | 0.899528i | \(-0.356089\pi\) | ||||
0.436864 | + | 0.899528i | \(0.356089\pi\) | |||||||
\(602\) | 4239.70 | 0.287039 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −61103.2 | −4.11631 | ||||||||
\(605\) | −8473.38 | −0.569408 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7117.15 | −0.475908 | −0.237954 | − | 0.971276i | \(-0.576477\pi\) | ||||
−0.237954 | + | 0.971276i | \(0.576477\pi\) | |||||||
\(608\) | 13900.9 | 0.927227 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1731.40 | −0.114922 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 173.297 | 0.0114183 | 0.00570913 | − | 0.999984i | \(-0.498183\pi\) | ||||
0.00570913 | + | 0.999984i | \(0.498183\pi\) | |||||||
\(614\) | 51173.5 | 3.36351 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 69715.5 | 4.55993 | ||||||||
\(617\) | 6102.75 | 0.398197 | 0.199099 | − | 0.979979i | \(-0.436199\pi\) | ||||
0.199099 | + | 0.979979i | \(0.436199\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14867.8 | −0.965409 | −0.482705 | − | 0.875783i | \(-0.660346\pi\) | ||||
−0.482705 | + | 0.875783i | \(0.660346\pi\) | |||||||
\(620\) | −11555.8 | −0.748534 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 40054.6 | 2.58206 | ||||||||
\(623\) | −3278.69 | −0.210847 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12951.6 | 0.828900 | ||||||||
\(626\) | −9772.64 | −0.623951 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13078.9 | 0.831056 | ||||||||
\(629\) | −731.475 | −0.0463686 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17210.6 | −1.08580 | −0.542902 | − | 0.839796i | \(-0.682675\pi\) | ||||
−0.542902 | + | 0.839796i | \(0.682675\pi\) | |||||||
\(632\) | −37550.3 | −2.36340 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16765.5 | −1.05023 | ||||||||
\(635\) | 3003.21 | 0.187683 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −92218.9 | −5.72254 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −6532.30 | −0.403456 | ||||||||
\(641\) | 12636.0 | 0.778616 | 0.389308 | − | 0.921108i | \(-0.372714\pi\) | ||||
0.389308 | + | 0.921108i | \(0.372714\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9586.37 | −0.587947 | −0.293973 | − | 0.955814i | \(-0.594978\pi\) | ||||
−0.293973 | + | 0.955814i | \(0.594978\pi\) | |||||||
\(644\) | −14950.2 | −0.914786 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −582.641 | −0.0354856 | ||||||||
\(647\) | −5244.32 | −0.318664 | −0.159332 | − | 0.987225i | \(-0.550934\pi\) | ||||
−0.159332 | + | 0.987225i | \(0.550934\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −29771.4 | −1.80066 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8206.39 | −0.492925 | ||||||||
\(653\) | −18869.0 | −1.13078 | −0.565392 | − | 0.824822i | \(-0.691275\pi\) | ||||
−0.565392 | + | 0.824822i | \(0.691275\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5662.59 | 0.337795 | ||||||||
\(656\) | −31539.3 | −1.87714 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 28889.3 | 1.71159 | ||||||||
\(659\) | 24299.8 | 1.43639 | 0.718197 | − | 0.695839i | \(-0.244967\pi\) | ||||
0.718197 | + | 0.695839i | \(0.244967\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29915.0 | 1.76030 | 0.880151 | − | 0.474694i | \(-0.157441\pi\) | ||||
0.880151 | + | 0.474694i | \(0.157441\pi\) | |||||||
\(662\) | −8335.03 | −0.489350 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −41347.1 | −2.41653 | ||||||||
\(665\) | −1069.24 | −0.0623508 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12162.6 | 0.706056 | ||||||||
\(668\) | 3155.69 | 0.182780 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 324.128 | 0.0186898 | ||||||||
\(671\) | 8005.86 | 0.460600 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15493.7 | 0.887426 | 0.443713 | − | 0.896169i | \(-0.353661\pi\) | ||||
0.443713 | + | 0.896169i | \(0.353661\pi\) | |||||||
\(674\) | −17115.8 | −0.978154 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11729.7 | −0.665891 | −0.332945 | − | 0.942946i | \(-0.608042\pi\) | ||||
−0.332945 | + | 0.942946i | \(0.608042\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22005.6 | 1.24374 | ||||||||
\(680\) | 769.698 | 0.0434067 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 74003.5 | 4.15505 | ||||||||
\(683\) | 1168.42 | 0.0654587 | 0.0327294 | − | 0.999464i | \(-0.489580\pi\) | ||||
0.0327294 | + | 0.999464i | \(0.489580\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3249.10 | −0.181229 | ||||||||
\(686\) | −37099.1 | −2.06480 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 10478.9 | 0.580675 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 32992.9 | 1.81637 | 0.908183 | − | 0.418574i | \(-0.137470\pi\) | ||||
0.908183 | + | 0.418574i | \(0.137470\pi\) | |||||||
\(692\) | −11196.7 | −0.615078 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 30679.2 | 1.67805 | ||||||||
\(695\) | −870.612 | −0.0475168 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 651.438 | 0.0354017 | ||||||||
\(698\) | −17856.3 | −0.968295 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −37192.2 | −2.00819 | ||||||||
\(701\) | 14785.8 | 0.796651 | 0.398326 | − | 0.917244i | \(-0.369591\pi\) | ||||
0.398326 | + | 0.917244i | \(0.369591\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4582.77 | 0.245864 | ||||||||
\(704\) | 83357.0 | 4.46255 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 66021.0 | 3.51945 | ||||||||
\(707\) | 13430.6 | 0.714442 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12634.0 | 0.669225 | 0.334612 | − | 0.942356i | \(-0.391395\pi\) | ||||
0.334612 | + | 0.942356i | \(0.391395\pi\) | |||||||
\(710\) | 4125.52 | 0.218067 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −14786.8 | −0.778312 | ||||||||
\(713\) | −9760.24 | −0.512656 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 46148.7 | 2.40874 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −45814.6 | −2.38132 | ||||||||
\(719\) | 27296.5 | 1.41584 | 0.707920 | − | 0.706292i | \(-0.249634\pi\) | ||||
0.707920 | + | 0.706292i | \(0.249634\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 19029.5 | 0.982936 | ||||||||
\(722\) | −33146.3 | −1.70856 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −79438.5 | −4.07777 | ||||||||
\(725\) | 30257.4 | 1.54997 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4658.21 | 0.237639 | 0.118819 | − | 0.992916i | \(-0.462089\pi\) | ||||
0.118819 | + | 0.992916i | \(0.462089\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −10718.4 | −0.543432 | ||||||||
\(731\) | −216.439 | −0.0109512 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −166.474 | −0.00838864 | −0.00419432 | − | 0.999991i | \(-0.501335\pi\) | ||||
−0.00419432 | + | 0.999991i | \(0.501335\pi\) | |||||||
\(734\) | 13393.9 | 0.673537 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −25219.4 | −1.26304 | ||||||||
\(737\) | −1498.74 | −0.0749074 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12738.1 | 0.634069 | 0.317035 | − | 0.948414i | \(-0.397313\pi\) | ||||
0.317035 | + | 0.948414i | \(0.397313\pi\) | |||||||
\(740\) | −9843.70 | −0.489002 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 854.092 | 0.0422570 | ||||||||
\(743\) | 30724.5 | 1.51705 | 0.758527 | − | 0.651641i | \(-0.225919\pi\) | ||||
0.758527 | + | 0.651641i | \(0.225919\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3043.76 | 0.149684 | ||||||||
\(746\) | −6131.38 | −0.300919 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −5786.84 | −0.282871 | ||||||||
\(749\) | 5193.37 | 0.253353 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −39538.6 | −1.92115 | −0.960575 | − | 0.278021i | \(-0.910322\pi\) | ||||
−0.960575 | + | 0.278021i | \(0.910322\pi\) | |||||||
\(752\) | 71403.2 | 3.46251 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7928.35 | 0.382175 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23035.1 | 1.10598 | 0.552990 | − | 0.833188i | \(-0.313487\pi\) | ||||
0.552990 | + | 0.833188i | \(0.313487\pi\) | |||||||
\(758\) | −65352.1 | −3.13153 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4822.23 | −0.230159 | ||||||||
\(761\) | −32454.0 | −1.54594 | −0.772968 | − | 0.634445i | \(-0.781229\pi\) | ||||
−0.772968 | + | 0.634445i | \(0.781229\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11784.6 | 0.559150 | ||||||||
\(764\) | −71986.8 | −3.40889 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 54616.1 | 2.57619 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32216.2 | −1.51072 | −0.755362 | − | 0.655307i | \(-0.772539\pi\) | ||||
−0.755362 | + | 0.655307i | \(0.772539\pi\) | |||||||
\(770\) | −14708.2 | −0.688372 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 97613.2 | 4.55075 | ||||||||
\(773\) | −2924.60 | −0.136081 | −0.0680404 | − | 0.997683i | \(-0.521675\pi\) | ||||
−0.0680404 | + | 0.997683i | \(0.521675\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24280.9 | −1.12541 | ||||||||
\(776\) | 99244.7 | 4.59108 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −31361.2 | −1.44519 | ||||||||
\(779\) | −4081.32 | −0.187713 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19076.1 | −0.874001 | ||||||||
\(782\) | 1057.04 | 0.0483374 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −22553.5 | −1.02740 | ||||||||
\(785\) | −1697.03 | −0.0771586 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 25507.1 | 1.15531 | 0.577656 | − | 0.816280i | \(-0.303967\pi\) | ||||
0.577656 | + | 0.816280i | \(0.303967\pi\) | |||||||
\(788\) | 60011.1 | 2.71295 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7922.16 | 0.356782 | ||||||||
\(791\) | −19444.7 | −0.874050 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −13416.8 | −0.599677 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1309.35 | 0.0583023 | ||||||||
\(797\) | −5448.98 | −0.242174 | −0.121087 | − | 0.992642i | \(-0.538638\pi\) | ||||
−0.121087 | + | 0.992642i | \(0.538638\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1474.82 | −0.0653008 | ||||||||
\(800\) | −62739.0 | −2.77270 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 49297.8 | 2.17053 | ||||||||
\(803\) | 49560.9 | 2.17804 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1939.85 | 0.0849324 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 60571.7 | 2.63726 | ||||||||
\(809\) | 2453.12 | 0.106610 | 0.0533048 | − | 0.998578i | \(-0.483025\pi\) | ||||
0.0533048 | + | 0.998578i | \(0.483025\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5133.85 | −0.222286 | −0.111143 | − | 0.993804i | \(-0.535451\pi\) | ||||
−0.111143 | + | 0.993804i | \(0.535451\pi\) | |||||||
\(812\) | −81191.4 | −3.50894 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 63039.4 | 2.71441 | ||||||||
\(815\) | 1064.81 | 0.0457651 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1356.01 | 0.0580673 | ||||||||
\(818\) | 49432.6 | 2.11292 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8766.61 | 0.373345 | ||||||||
\(821\) | 23854.0 | 1.01402 | 0.507009 | − | 0.861941i | \(-0.330751\pi\) | ||||
0.507009 | + | 0.861941i | \(0.330751\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 757.156 | 0.0320690 | 0.0160345 | − | 0.999871i | \(-0.494896\pi\) | ||||
0.0160345 | + | 0.999871i | \(0.494896\pi\) | |||||||
\(824\) | 85822.6 | 3.62836 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −36302.2 | −1.52919 | ||||||||
\(827\) | −28621.2 | −1.20345 | −0.601726 | − | 0.798702i | \(-0.705520\pi\) | ||||
−0.601726 | + | 0.798702i | \(0.705520\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27429.2 | 1.14916 | 0.574582 | − | 0.818447i | \(-0.305165\pi\) | ||||
0.574582 | + | 0.818447i | \(0.305165\pi\) | |||||||
\(830\) | 8723.19 | 0.364803 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 465.838 | 0.0193761 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −409.462 | −0.0169701 | ||||||||
\(836\) | 36255.1 | 1.49989 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 34840.7 | 1.43622 | ||||||||
\(839\) | 4633.62 | 0.190668 | 0.0953339 | − | 0.995445i | \(-0.469608\pi\) | ||||
0.0953339 | + | 0.995445i | \(0.469608\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 41663.6 | 1.70829 | ||||||||
\(842\) | 16413.7 | 0.671798 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −21813.0 | −0.889614 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 47775.0 | 1.93810 | ||||||||
\(848\) | 2110.99 | 0.0854853 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 2629.64 | 0.106113 | ||||||||
\(851\) | −8314.19 | −0.334908 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14854.6 | −0.596261 | −0.298131 | − | 0.954525i | \(-0.596363\pi\) | ||||
−0.298131 | + | 0.954525i | \(0.596363\pi\) | |||||||
\(854\) | 9762.07 | 0.391161 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 23421.9 | 0.935216 | ||||||||
\(857\) | 42799.5 | 1.70595 | 0.852977 | − | 0.521948i | \(-0.174794\pi\) | ||||
0.852977 | + | 0.521948i | \(0.174794\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8246.47 | −0.327551 | −0.163775 | − | 0.986498i | \(-0.552367\pi\) | ||||
−0.163775 | + | 0.986498i | \(0.552367\pi\) | |||||||
\(860\) | −2912.70 | −0.115491 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −42580.1 | −1.68246 | ||||||||
\(863\) | −17695.4 | −0.697983 | −0.348991 | − | 0.937126i | \(-0.613476\pi\) | ||||
−0.348991 | + | 0.937126i | \(0.613476\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1452.81 | 0.0571064 | ||||||||
\(866\) | 39132.3 | 1.53553 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 65154.2 | 2.54779 | ||||||||
\(869\) | −36631.4 | −1.42996 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 53148.2 | 2.06402 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6622.49 | −0.256303 | ||||||||
\(875\) | 9949.64 | 0.384411 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −14346.8 | −0.552401 | −0.276200 | − | 0.961100i | \(-0.589075\pi\) | ||||
−0.276200 | + | 0.961100i | \(0.589075\pi\) | |||||||
\(878\) | 81622.7 | 3.13739 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −36353.0 | −1.39257 | ||||||||
\(881\) | 2063.51 | 0.0789121 | 0.0394560 | − | 0.999221i | \(-0.487437\pi\) | ||||
0.0394560 | + | 0.999221i | \(0.487437\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −34137.1 | −1.30103 | −0.650513 | − | 0.759495i | \(-0.725446\pi\) | ||||
−0.650513 | + | 0.759495i | \(0.725446\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8138.58 | −0.308602 | ||||||||
\(887\) | 22238.5 | 0.841821 | 0.420910 | − | 0.907102i | \(-0.361711\pi\) | ||||
0.420910 | + | 0.907102i | \(0.361711\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16932.8 | −0.638817 | ||||||||
\(890\) | 3119.63 | 0.117495 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 48075.0 | 1.80456 | ||||||||
\(893\) | 9239.89 | 0.346250 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5987.96 | −0.223637 | ||||||||
\(896\) | 36830.7 | 1.37325 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3783.45 | 0.140596 | ||||||||
\(899\) | −53005.7 | −1.96645 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −43.6019 | −0.00161220 | ||||||||
\(902\) | −56141.7 | −2.07241 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −87694.9 | −3.22643 | ||||||||
\(905\) | 10307.4 | 0.378597 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44160.3 | −1.61667 | −0.808335 | − | 0.588723i | \(-0.799631\pi\) | ||||
−0.808335 | + | 0.588723i | \(0.799631\pi\) | |||||||
\(908\) | −78953.8 | −2.88565 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11916.3 | −0.433376 | −0.216688 | − | 0.976241i | \(-0.569525\pi\) | ||||
−0.216688 | + | 0.976241i | \(0.569525\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −40335.3 | −1.46211 | ||||||||
\(914\) | −39043.0 | −1.41294 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −89793.0 | −3.23891 | ||||||||
\(917\) | −31927.1 | −1.14975 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20128.9 | −0.722516 | −0.361258 | − | 0.932466i | \(-0.617653\pi\) | ||||
−0.361258 | + | 0.932466i | \(0.617653\pi\) | |||||||
\(920\) | 8748.64 | 0.313515 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −10525.0 | −0.375945 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20683.5 | −0.735210 | ||||||||
\(926\) | −55654.1 | −1.97506 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −136961. | −4.84478 | ||||||||
\(929\) | 31428.4 | 1.10994 | 0.554969 | − | 0.831871i | \(-0.312730\pi\) | ||||
0.554969 | + | 0.831871i | \(0.312730\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2918.52 | −0.102740 | ||||||||
\(932\) | −109715. | −3.85605 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −47150.1 | −1.65182 | ||||||||
\(935\) | 750.863 | 0.0262629 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 42473.2 | 1.48083 | 0.740416 | − | 0.672149i | \(-0.234629\pi\) | ||||
0.740416 | + | 0.672149i | \(0.234629\pi\) | |||||||
\(938\) | −1827.51 | −0.0636144 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −19847.1 | −0.688661 | ||||||||
\(941\) | 42644.0 | 1.47732 | 0.738659 | − | 0.674079i | \(-0.235459\pi\) | ||||
0.738659 | + | 0.674079i | \(0.235459\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7404.46 | 0.255697 | ||||||||
\(944\) | −89725.0 | −3.09354 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18653.0 | 0.641080 | ||||||||
\(947\) | −4282.95 | −0.146966 | −0.0734831 | − | 0.997296i | \(-0.523412\pi\) | ||||
−0.0734831 | + | 0.997296i | \(0.523412\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −16475.0 | −0.562651 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4339.74 | −0.147744 | ||||||||
\(953\) | −40593.9 | −1.37982 | −0.689908 | − | 0.723897i | \(-0.742349\pi\) | ||||
−0.689908 | + | 0.723897i | \(0.742349\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9340.54 | 0.316495 | ||||||||
\(956\) | −32166.1 | −1.08821 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 59771.9 | 2.01581 | ||||||||
\(959\) | 18319.2 | 0.616850 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12744.8 | 0.427808 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −102198. | −3.41448 | ||||||||
\(965\) | −12665.7 | −0.422510 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17709.4 | 0.588931 | 0.294466 | − | 0.955662i | \(-0.404858\pi\) | ||||
0.294466 | + | 0.955662i | \(0.404858\pi\) | |||||||
\(968\) | 215464. | 7.15420 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −20938.1 | −0.693074 | ||||||||
\(971\) | −4038.97 | −0.133488 | −0.0667440 | − | 0.997770i | \(-0.521261\pi\) | ||||
−0.0667440 | + | 0.997770i | \(0.521261\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4908.72 | 0.161733 | ||||||||
\(974\) | −105366. | −3.46626 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 24128.1 | 0.791312 | ||||||||
\(977\) | 2764.30 | 0.0905197 | 0.0452598 | − | 0.998975i | \(-0.485588\pi\) | ||||
0.0452598 | + | 0.998975i | \(0.485588\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14424.9 | −0.470912 | ||||||||
\(980\) | 6268.93 | 0.204340 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18295.4 | 0.594531 | ||||||||
\(983\) | 17804.5 | 0.577695 | 0.288848 | − | 0.957375i | \(-0.406728\pi\) | ||||
0.288848 | + | 0.957375i | \(0.406728\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7786.65 | −0.251881 | ||||||||
\(986\) | 5740.57 | 0.185413 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2460.12 | −0.0790974 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8129.69 | −0.260593 | −0.130297 | − | 0.991475i | \(-0.541593\pi\) | ||||
−0.130297 | + | 0.991475i | \(0.541593\pi\) | |||||||
\(992\) | 109908. | 3.51772 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −23260.7 | −0.742237 | ||||||||
\(995\) | −169.893 | −0.00541302 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −29452.9 | −0.935589 | −0.467795 | − | 0.883837i | \(-0.654951\pi\) | ||||
−0.467795 | + | 0.883837i | \(0.654951\pi\) | |||||||
\(998\) | −26997.7 | −0.856309 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1521.4.a.bk.1.10 | 10 | ||
3.2 | odd | 2 | 507.4.a.r.1.1 | 10 | |||
13.2 | odd | 12 | 117.4.q.e.82.5 | 10 | |||
13.7 | odd | 12 | 117.4.q.e.10.5 | 10 | |||
13.12 | even | 2 | inner | 1521.4.a.bk.1.1 | 10 | ||
39.2 | even | 12 | 39.4.j.c.4.1 | ✓ | 10 | ||
39.5 | even | 4 | 507.4.b.i.337.10 | 10 | |||
39.8 | even | 4 | 507.4.b.i.337.1 | 10 | |||
39.20 | even | 12 | 39.4.j.c.10.1 | yes | 10 | ||
39.38 | odd | 2 | 507.4.a.r.1.10 | 10 | |||
156.59 | odd | 12 | 624.4.bv.h.49.3 | 10 | |||
156.119 | odd | 12 | 624.4.bv.h.433.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.c.4.1 | ✓ | 10 | 39.2 | even | 12 | ||
39.4.j.c.10.1 | yes | 10 | 39.20 | even | 12 | ||
117.4.q.e.10.5 | 10 | 13.7 | odd | 12 | |||
117.4.q.e.82.5 | 10 | 13.2 | odd | 12 | |||
507.4.a.r.1.1 | 10 | 3.2 | odd | 2 | |||
507.4.a.r.1.10 | 10 | 39.38 | odd | 2 | |||
507.4.b.i.337.1 | 10 | 39.8 | even | 4 | |||
507.4.b.i.337.10 | 10 | 39.5 | even | 4 | |||
624.4.bv.h.49.3 | 10 | 156.59 | odd | 12 | |||
624.4.bv.h.433.3 | 10 | 156.119 | odd | 12 | |||
1521.4.a.bk.1.1 | 10 | 13.12 | even | 2 | inner | ||
1521.4.a.bk.1.10 | 10 | 1.1 | even | 1 | trivial |